Sustainable growth with renewable and non-renewable energy sources

How to control climate change and to spur clean energy are among the most important challenges facing the world today. So far, a large strand of literature on climate change states that we need two economic policy instruments to correct for the two types of market failures: an environmental tax on the carbon emissions and a research subsidy for research and development (R&D) spillovers in the renewable energy sector. The objective of our paper is to show that we need only one instrument, a research subsidy, on renewable energy, to switch from non-renewable energy to the renewable one. For doing so, we work on the elasticity of substitution between renewable and non-renewable energies and we show that investment in renewable energy modify the elasticity of substitution. Moreover, this paper provide the answer to the current puzzle on the trade-off between economic growth and the protection of environmental quality: we show that investment in renewable energy technologies increase economic productivity and GDP through more efficient processes. We emphasize the crucial role of R&D on clean energy for allowing the economy to overcome the environmental constraints.The paper consider a Schumpeterian model of endogenous growth to consider that production emit pollutants. The final good is produced employing labor, renewable energy and non-renewable energy. The two kinds of energy sources are imperfect substitutes. The produced quantity of non-renewable energy is a function of its resource price. In our framework, we do not model R&D in the non-renewable energy sector: the price of the non-renewable energy will rise since its resource is exhaustible. Broadly, the price of the non-renewable energy follows the generalized version of the Hotelling rule. The produced quantity of renewable energy depends on the learning function and indirectly both on the investment in R&D and on the skill labor engaged in R&D. The big push in the technology of the renewable need a non-linear jump, that is, there is a critical R&D threshold beyond which renewable energy gain in importance with respect to the dirty input. There is of course some uncertainty about the possibility to reach such a threshold and so investors do not know when the technological jump will happen. Labor is competitively engaged both in R&D activities aimed at designing higher-quality clean technology and generic labor (the one who enters in the final output production function). We first present the decentralized economy and study the behavior of agents in each sector: the final good sector, the R&D sector, the consumers and the government. We characterize both the decentralized equilibrium and the first-best optimum solutions. Next, we show how the optimum can be implemented by an appropriate public tool. We expect to show that, even if the economy faces two market failures, global warming and R&D spillovers, the social planner needs only one type of public tool to correct them, that is a subsidy for the renewable R&D sector. We show also that this strategy leads to a positive economic growth rate.